Math 375 Fall 2020

Math 375 Course Objectives

I. Basic Counting (Combinatorics)

B.1 I can apply the Addition Principle and the Multiplication Principle appropriately to counting problems.

II. Logic and Proof

L.1 I can prove the logical equivalence of two propositions using a truth table and using rules of logic.

L.2 I can write equivalent forms of a mathematical statement that involve quantifiers and negation.

L.3 I can give a direct proof of a mathematical statement.

L.4 I can prove a mathematical statement using mathematical induction.

III. Set Theory

S.1 I understand and can perform basic set operations.

S.2 I can determine and prove whether one set is a subset of or is equal to another set.

S.3 I understand properties of relations such as reflexivity, symmetry and transitivity.

S.4 I understand the definition of an equivalence relation and of equivalence classes.

S.5 I understand the relationship between equivalence relations and partitions.

IV. Group Theory

G.1 I understand the definition of a group.

G.2 I can find the cosets of a subgroup of a group.

V. Coding Theory

C.1 I can use basic methods to decode messages.

C.2 I can use a parity-check matrix to decode messages.

C.3 I can use coset leaders to decode messages.